# How many moles of gas occupy a 3.45-L container at a pressure of 150 kPa and a temperature of 45.6°C?

Feb 16, 2017

$\text{0.026 moles}$

#### Explanation:

Your tool of choice here will be the ideal gas law equation, which looks like this

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{P V = n R T}}}$

Here

• $P$ is the pressure of the gas
• $V$ is the volume it occupies
• $n$ is the number of moles of gas present in the sample
• $R$ is the universal gas constant, equal to $0.0821 \left(\text{atm L")/("mol K}\right)$
• $T$ is the absolute temperature of the gas

Now, it's important to realize that the units you have for the volume, pressure, and temperature of the gas must match the unit used in the expression of the universal gas constant.

In this case, you have

$\underline{\textcolor{w h i t e}{a a a a \textcolor{b l a c k}{\text{What you have")aaaaaaaaaacolor(black)("What you need}} a a a a a}}$

color(white)(aaaaaacolor(black)("liters " ["L"])aaaaaaaaaaaaaaacolor(black)("liters " ["L"])aaaa)color(darkgreen)(sqrt())

color(white)(aaacolor(black)("kilopascals " ["kPa"])aaaaaaaaacolor(black)("atmospheres " ["atm"])aaa)color(red)(xx)

color(white)(acolor(black)("degrees Celsius " [""^@"C"])aaaaaaaaaacolor(black)("Kelvin " ["K"])aaaa)color(red)(xx)

This means that in order to use the ideal gas law equation with the given value for the universal gas constant, you must convert the pressure and the temperature of the gas by using the conversion factors

color(blue)(ul(color(black)("1 atm = 760 kPa")))" " and " " color(blue)(ul(color(black)(T["K"] = t[""^@"C"] + "273.15")))

Rearrange the ideal gas law equation to solve for $n$

$P V = n R T \implies n = \frac{P V}{R T}$

Plug in your values to find -- do not forget the conversion factors!

$n = \left(\frac{150}{760} \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{atm"))) * 3.45 color(red)(cancel(color(black)("L"))))/(0.0821 (color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (45.6 + 273.15)color(red)(cancel(color(black)("K}}}}\right)$

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{0.026 moles}}}}$

The answer is rounded to two sig figs, the number of sig figs you have for the pressure of the gas.